This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Fast imaging techniques using non- Cartesian k-space trajectories, e.g. spiral, have been implemented to reduce the long scan times associated with volumetric MRSI. The scan time can be further reduced by acquiring partial k-space data with multiple receiving coils and reconstruct using the knowledge of each coil's sensitivity profile. With k-space data on a Cartesian grid, reconstruction can be achieved using image-domain based SENSE algorithm or k-space-domain based GRAPPA algorithm. For non-Cartesian k-space data, image-domain based iterative SENSE algorithm or k-space-domain based PARS algorithm can be used for the reconstruction. Although effective, these non-Cartesian k-space data reconstruction methods suffer from long computing times. In this work, we propose a parallel MRSI reconstruction method with arbitrary trajectories using k-space sparse matrices (KSPA). The algorithm achieves reduced computing times and memory requirements by taking advantage of the compactness of the convolution kernel defined by the coil sensitivity. Reconstruction using this algorithm is demonstrated using undersampled spiral k-space data from an in-vivo study with different reduction factors. Methods and Discussion: To encode chemical shift information, fast MRSI with spiral k-space trajectories samples data points on repeated spiral trajectories. With the KSPA algorithm, the reconstruction matrix is calculated using k-space data on the first spiral trajectory and then applied to k-space data on the remaining spiral trajectories to estimate the fully sampled k-space data on repeated Cartesian grids. Since the reconstruction matrix only needs to be computed once, significant reconstruction time can be reduced.